"I didn't think that a machine this old would have a
If by that you mean a reversing motor, then yes, they've been around since the beginning of time. Maytag, GE, Easy and all kinds of machine, anything really that spin-drains used a reversing motor.
If you mean that the motor reverses for each agitation stroke, then this one does not do that to my knowledge, it has a gear-transmission (large red thing).
-Tim